1D DWT basis functions for incomplete decomposition (e.g. 1-level)

Haar wavelets

Haar low-pass filter

haar = HaarFilter[]

RowBox[{{, RowBox[{0.707107, ,, 0.707107}], }}]

Haar high-pass filter

HighPassFilter[haar]

RowBox[{{, RowBox[{0.707107, ,, RowBox[{-, 0.707107}]}], }}]

Example Haar-wavelet basis functions for 1-level DWT

zeros = Table[0, {16}] ;

Table[ListPlot[InverseWavelet1D[ReplacePart[zeros, 1, i], haar, 1], PlotRangeAll, Plot ... 54;True, PlotStyle {Red, Thickness[.005]}, ImageSize288], {i, 1, Length[zeros]}] ;

[Graphics:../HTMLFiles/index_23.gif]

(Web: click on image to see all 64 basis functions)

Created by Mathematica  (February 16, 2004)